Qureshi, M. I.; Malik, Shakir Hussain; Shah, Tafaz ul Rahman Hypergeometric representations of some mathematical functions via Maclaurin series. (English) Zbl 1474.33004 Jñānābha 50, No. 1, 179-188 (2020). Summary: In this paper, by using Maclaurin series of a given mathematical function and expressing the coefficient of the general term of the corresponding Maclaurin series in form of Pochhammer symbols, we obtain the hypergeometric forms of following functions: \[ \frac{\sin^{-1}(x)}{\sqrt{(1-x^2)}},[\sin^{-1}(x)]^2,\sin^{-1}(x),\frac{\sinh^{-1}(x)}{\sqrt{(1+x^2)}},[\sinh^{-1}(x)]^2,\sinh^{-1}(x)\text{ and }\ln\{e(1-x)^{\frac{1}{x}}\}^{-\frac 2x}. \] Cited in 2 Documents MSC: 33B10 Exponential and trigonometric functions Keywords:hypergeometric functions; Leibnitz theorem; Maclaurin series; Pochhammer symbol PDFBibTeX XMLCite \textit{M. I. Qureshi} et al., Jñānābha 50, No. 1, 179--188 (2020; Zbl 1474.33004) Full Text: Link